Full UV wrapping on a mirrored Mesh
Yes, this is possible (out of the box).  The mirror modifier has a mirror UV option, so you can mirror either the U or V (or both) texture coordinates.  So for example, you can model the left hand side of a head with the mirror modifier enabled for X and U.  Then unwrap it to the left-hand side of your texture.  The mirrored right-hand side of the mesh will have its UV co-ordinates on the right-hand side of the texture, so you can have something different there, e.g. a scar drawn on the texture's right cheek which appears on the right cheek of the mirrored model.